Related papers: Ground subgroups
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…
We determine the fundamental group of period domains over finite fields.
For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.
In this paper, we discuss a group-theoretical generalization of the well-known Gauss formula involving the functionthat counts the number of automorphisms of a finite group. This gives several characterizations of finite cyclic groups.
The aim of this article is to discuss and clarify the notion of fractality for subgroups of the group of automorphisms of a regular rooted tree. For this purpose we define three types of fractality. We show that they are not equivalent, by…
We give a complete list of the one-dimensional groups definable in algebraically closed valued fields and i the pseudo-local fields, up to a finite index subgroup and a quotient by a finite subgroup.
This paper describes a simple method for estimating lower bounds on the number of classes of equivalence for a special kind of integer sequences, called division sequences. The method is based on adding group structure to classes of…
In this paper, we are interested in study subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalized covering subgroups and the other famous…
We consider the problem of the explicit description of the gauge-invariant subspace of pure lattice gauge theories in the Hamiltonian formulation, where the gauge group is either a compact Lie group or a finite group. The latter case is…
This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of…
A random graph of free groups contains a surface subgroup
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
We classify pointed spaces according to the first fundamental group of their reduced suspension. A pointed space is either of so-called totally path disconnected type or of horseshoe type. These two camps are defined topologically but a…
Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies the bound $|H|^3 \ge |G|$. In this note we determine all the large maximal subgroups of finite simple groups, and we establish an…
We define the notion of accessibility for a pro-$p$ group. We prove that finitely generated pro-$p$ groups are accessible given a bound on the size of their finite subgroups. We then construct a finitely generated inaccessible pro-$p$…
We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.
We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation…
The assignment of local observables in the vacuum sector, fulfilling the standard axioms of local quantum theory, is known to determine uniquely a compact group G of gauge transformations of the first kind together with a central involutive…
It is known that in any free group the isolator of finitely generated subgroup is finitely generated subgroup. A very simple proof of this statement is proposed.
In this paper, we define locally matchable subsets of a group which is derived from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…